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Stuff thats darker looks further away. That is to say that where there is a gradient from light to dark the dark side is farther. It takes a little skill to have multiple layers shaded so that it looks 3D but for a single chasm just start the top of cliff as is but fade down to very dark at bottom. For this instance, ignore the light direction and use the shading to give the depth perception. You have a little there - just up it a lot.

The bridge gives you a tailor-made way to shade for depth. Manually make you a gray copy of the whole bridge shape, shift it along the river one way or the other - though down and to the right will give the most "automatic" effect. Copy the shadow. Clip one copy to just the water shape, and slightly ripple-distort that one to match the water's ripples. Clip the other one to everything BUT the water, and warp it so it matches the water-shadow at shorelines, and bridge abutments at cliff's edge.

So far you have an indication the river is below, just not how far. Now, if your bridge uprights might be 12 feet high, to make the water look 100 feet below, give the bridge uprights shadows that are 1/8 the offset you gave the canyon-bottom shadow. If they're twenty feet tall, use 1/5 the offset, and so forth. If the angle of light would put post shadows on cliffside or water, include the length they would cast in the river-bottom or wall shadow layer.

If the angle you're casting shadows at permits, you can darken and brighten sections of canyon wall to put them in shade or full(er) sunshine. As for your canyon-wall pattern, most anything it's made of other than 'devil's postpile' crystals will look from straight above to be stretched vertically - you should probably see some lines from top toward bottom, even if not necessarily all the way.

Also, things get smaller the further away they are. You need some visual cues to provide scale so like put a dead guy at the bottom so that we can tell how big the river is. Personally, I'd just make the river thinner.

If the radiance of a thousand suns was to burst at once into the sky, that would be like the splendor of the Mighty One...I am become Death, the Shatterer of worlds.
-J. Robert Oppenheimer (father of the atom bomb) alluding to The Bhagavad Gita (Chapter 11, Verse 32)

made a quick example for you so you can see how shadows will help with depth ... its a lot easier when you have the original layers to work with. Remember, everything cast shadows, and the light always comes from the same place (outdoors in the sun at least) - so even the ropes to tie the bridge off with casts shadows, small dark ones where the rope is low, softer/wider ones where the rope is higher.